Scale e ects in a distributed snow water equivalence and snowmelt model for mountain basins

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1 Hydrological Processes Hydrol. Process. 12, 1527±1536 (1998) Scale e ects in a distributed snow water equivalence and snowmelt model for mountain basins Don Cline, 1 * Kelly Elder 2 and Roger Bales 3 1 National Operational Hydrologic Remote Sensing Center, O ce of Hydrology, National Weather Service, NOAA, USA 2 Department of Earth Resources, Colorado State University, Fort Collins, CO, USA 3 Department of Hydrology and Water Resources, University of Arizona, Tucson, AZ, USA Abstract: We investigated the e ect of increasing spatial and temporal resolutions on modelled distributions of snow water equivalence (SWE) and snowmelt in the Emerald Lake Watershed (ELW) of the Sierra Nevada of California, USA. We used a coupled remote sensing/distributed energy balance snowmelt model (SNODIS), and used previously validated results from a high spatial (30 m) and temporal (hourly) resolution model run in ELW as a control. We selected spatial resolutions that are commensurate with standard product DEMs (digital elevation models) or with existing or planned satellite remote sensing data, and temporal resolutions that are factors of typical operational intervals for meteorological data. We degraded the spatial resolution of the DEM from 30 m to 90, 250 and 500 m prior to computing the distributed micrometeorological data. We degraded the classi ed remote sensing data to the same spatial resolutions prior to computing the duration of the snow cover. Similarly, we degraded the temporal resolution of the micrometeorological data from 1 h to 3 and 6 h prior to computing the distributed energy balance and snowmelt. We compared mean basin SWE, basin snowpack water volume and the spatial patterns of SWE from each test with our previous, high resolution results. We found no signi cant di erences between the mean basin-wide SWE computed from the 250 m and 500 m spatial resolutions and that of our high resolution control, regardless of temporal resolution. At each temporal resolution mean basin SWE was overestimated at the 90 m resolution by 14±17%. Coarsening of the spatial resolution did result in a loss of explicit information regarding the location of SWE in the basin, as expected. We discuss these results in terms of their implications for applying the SNODIS model to larger regions. # 1998 John Wiley & Sons, Ltd. KEY WORDS scale e ects; snow water equivalence; mountain basins; SNODIS; spatial and temporal resolution INTRODUCTION Although the importance of water stored in mountain snowpacks is widely recognized, we lack adequate methods of assessing the magnitude of this resource and forecasting its release over time. For over 40 years simple empirical techniques have been used operationally to estimate the volume of snowmelt runo with reasonable success, but empirical techniques generally provide little information about the timing or rate of snowmelt runo. A major limitation of such empirical techniques is their dependence on boundary conditions governing the development of calibration parameters. This dependence may cause such methods to fail in extreme or unusual years, which often are the years of particular interest. When calibrating * Correspondence to: Dr. D. Cline, National Operational Hydrologic Remote Sensing Center, O ce of Hydrology, National Weather Service, NOAA, USA. Contract grant sponsor: NASA Earth Observing System; National Science Foundation; National Weather Service, O ce of Hydrology. Contract grant number: EAR CCC 0885±6087/98/111527±10$1750 Received 22 May 1997 # 1998 John Wiley & Sons, Ltd. Revised 22 March 1998 Accepted 27 March 1998

2 1528 D. CLINE ET AL. snowmelt±runo models, parameters are typically optimized to produce good ts between observed and simulated stream ow. Since many factors in uence stream ow besides SWE and snowmelt characteristics, such models are forced to accommodate a variety of possible biases built into the model parameters. This can result in false compensation of incorrect estimates of SWE and snowmelt by model parameters related to other processes. A third limitation common to most empirical SWE and snowmelt models is a dependence on a small number of ground SWE observations within a basin of interest, and the degree to which those observations may or may not be representative of the snowpack conditions elsewhere in the basin. These examples are just some of the many problems and di culties associated with current operational snowpack assessment and snowmelt±runo forecasting techniques. To help address these problems, we developed a physically based, spatially distributed model to estimate the spatial distribution of SWE and snowmelt in mountain basins (SNODIS) (Cline et al., 1997). The SNODIS model couples remotely sensed snow cover duration information with a spatial energy balance model to back-calculate, at the end of a snowmelt season, the distribution of SWE at peak accumulation and the distribution of snowmelt through the season. The SNODIS model is based on the simple conceptual idea that the duration of snow cover during the ablation season at a particular location is a function of: (1) the amount of SWE at that location at the beginning of the ablation season; and (2) the total energy available to melt the snow through the course of the season. SNODIS uses a time-series of remotely sensed imagery to determine the duration of snow cover on every pixel, and uses a spatial energy balance model to determine how much energy is available to melt snow over time. Short-wave and long-wave radiation exchanges, and turbulent energy exchanges are modelled at every pixel. The SNODIS model provides an estimate of the distribution of SWE without ground observations of SWE or discharge measurements. Thus it provides an independent, physically based estimate of the distribution of SWE and snowmelt that could be used to improve estimates of water resources stored in mountain snowpacks, to improve estimates of the timing, rate, and magnitude of snowmelt runo, and to provide SWE information to assist calibration of operational conceptual snowmelt±runo models. Our initial test of the SNODIS model was at the Emerald Lake Watershed (ELW) in the Sierra Nevada of California (Cline et al., 1997). We initially tested SNODIS under conditions of high spatial (30 m) and high temporal (hourly) resolutions. We found that under these conditions SNODIS produced an estimate of the magnitude and distribution of SWE at peak accumulation that compared well with results from previous methods, snow course data and models of SWE based on eld measurements. We statistically compared the spatial mean and variance of the SNODIS-modelled peak accumulation SWE distribution with 180 snow course measurements in the basin (Melack et al., 1996) and found no signi cant di erences. We compared the modelled spatial patterns of SWE with measured patterns from previous years (Elder et al., 1991), and found only small di erences that would be expected from interannual variations in SWE distributions. We compared the SNODIS-modelled total basin SWE volume with results from a binary regression tree SWE distribution model that is based on eld measurements, and that had been successfully developed and tested in the same basin (SWETREE) (Elder, 1995; Elder et al., 1995). The total basin water volume stored as snow agreed within 1% between the two methods. Based on these initial successful results and the physical nature of the model, we concluded that SNODIS should be applicable over larger mountain regions. Before this is possible, several problems must rst be addressed, such as the extrapolation of meteorological data over larger regions, and the representation of the spatial distributions of energy balance terms and SWE at the coarser spatial and temporal scales necessary for computational e ciency. We focus on the latter in this study. As a rst step towards extending the SNODIS model to larger regions, this paper evaluates the e ects of increasing spatial and temporal resolutions on distributions of SWE and snowmelt modelled by SNODIS. Larger resolutions would be desirable for regional-scale modelling, principally to reduce computational and data requirements, particularly for operational applications. We tested spatial resolutions that are commensurate with standard product digital elevation models (DEMs) or with existing or planned satellite remote sensing data, and temporal resolutions that are factors of typical operational intervals for

3 SCALE EFFECTS 1529 meteorological data. The successful results under high resolution conditions permit us to treat the original model run as a control against which we can compare new model runs that test conditions of coarser spatial and temporal resolutions. METHODS We used the original, high resolution (30 m spatial resolution, hourly temporal resolution) SNODIS results for the 1993 water year at the ELW (Cline et al., 1997) as a control against which to compare the results of this sensitivity study. The ELW is a small (120 ha) high alpine basin in Sequoia National Park, Sierra Nevada, California (Figure 1). The basin relief is 636 m, and the entire watershed lies above the tree-line. Tonnessen (1991) describes the watershed in detail. We modelled the spatial distribution of SWE near peak accumulation and the onset of snowmelt (21 April 1993). The overall modelling approach is illustrated in Figure 2. We mapped fractional (subpixel) snow cover at three dates (4 April, 5 May and 22 June, 1993) using Landsat Thematic Mapper (TM) and the spectral unmixing algorithm of Rosenthal and Dozier (1996). We modelled hourly incident solar radiation using a two-stream radiative transfer model for rugged terrain (TOPORAD) (Dozier and Frew, 1990). Using a 30 m DEM, we extrapolated hourly air temperature, relative humidity and wind speed across the basin from a micrometeorological instrument site located near the outlet of the basin. We modelled incident long-wave radiation as a function of the previously extrapolated air temperature and relative humidity using the Idso2 formulation (Idso, 1981). We considered the energy balance of the snowpack each hour at each pixel as DQ S DQ M ˆ K* L* Q E Q H Q G Q R 1 where DQ S is the convergence or divergence of sensible heat uxes within the snowpack volume, DQ M is the change in latent heat due to melting or freezing, K* is the net short-wave radiation ux, L* is the net longwave radiation ux, Q H is the sensible heat ux, Q E is the latent heat ux, Q G is the ground heat ux and Q R is the heat advected by precipitation. If the snowpack is below 0 8C, changes in the residual energy term Figure 1. Map showing Emerald Lake Watershed (ELW) study area

4 1530 D. CLINE ET AL. Figure 2. Flowchart showing modelling structure with three main components: (1) determination of fractional snow cover at subpixel levels using spectral unmixing and decision trees; (2) computation of the energy balance at each pixel using estimated micrometeorological data distributions; and (3) coupling the two via the cumulative energy available to melt snow over time to determine the initial SWE at the beginning of the model run at each pixel DQ S DQ M result in a temperature change within the snowpack. If the snowpack is at 0 8C, subsequent net energy losses will act to cool the snowpack or refreeze liquid water, while net energy gains will result in snowmelt. We considered the ground heat ux to be negligible, and precipitation recorded during the modelling period was also negligible so was not a factor in this study. We modelled the turbulent uxes using the bulk aerodynamic algorithms in SNTHERM89.rev4 (Jordan, 1991). To solve the terms on the righthand side of Equation (1) we made assumptions concerning the change of albedo over time, snow surface temperatures, snow emissivities and the roughness length of the snowpack. To compute K*, we assumed a spatially constant snow surface albedo that decreased over time using a simple decay function. To compute L* andq H, we modelled snow surface temperatures as functions of air temperature, using a lag during the daytime, and a reduction at night of 4±6 8C. However, modelled air temperatures remained well above 0 8C for most of the study period, so snow surface temperatures were usually simply constrained to 0 8C. We assumed a snow surface emissivity of 0.99 for computing surface long-wave emissions using the Stefan± Boltzmann equation. To compute the turbulent uxes we assumed a roughness length of m. Starting from 21 April, we computed a running total of the residual energy term, DQ S DQ M, for each pixel to provide a value for the total energy available to melt snow at each time-step. At the time of each remote sensing scene, the total energy for snowmelt at each pixel was weighted by the fractional area of the pixel that had become snow free since the previous remote sensing date, and converted to mass units to determine the amount of SWE that would have existed on that fraction of the pixel at the beginning of the model run. In the present study we duplicated the above methodology used by Cline et al. (1997), with the exception that we systematically modi ed the spatial and temporal resolutions of the data used in the model to perform a series of sensitivity tests. We degraded the spatial resolution of the DEM from 30 m to 90, 250 and 500 m using a nearest neighbor algorithm prior to computing the distributed micrometeorological data (Figure 3). This approach mimics a surface sampling approach commonly used in photogrammetric DEM production. We degraded the classi ed remote sensing data to the same spatial resolutions prior to computing the duration of the snow cover. Since these data lie in a range from 0 to 1, a spatial averaging algorithm was used

5 SCALE EFFECTS 1531 Figure 3. Views of degraded DEM data: (a) 30 m resolution, (b) 90 m, (c) 250 m and (d) 500 m. The views are looking from the north±north-west to the south±south-east that resulted in the new, larger pixels having a fractional snow-covered area equal to the sum of the snowcovered areas of the smaller component pixels. We degraded the temporal resolution of the micrometeorological data from 1 h to 3 and 6 h prior to computing the distributed energy balance and snowmelt. We simply discarded the unneeded observations, retaining every third or every sixth observation (beginning at midnight) accordingly. Since the recording and averaging formats and intervals of meteorological data are variable, we considered this method of degrading the temporal resolution representative of the crudest data likely to be used. We completed a total of nine tests, estimating the distribution of SWE and snowmelt for each paired combination of 90, 250 and 500 m spatial resolutions and 1, 3 and 6 h temporal resolutions. For each test, we compared the arithmetic mean basin SWE (SWE), the total basin volume of SWE, the spatial pattern of SWE standardized to zero mean and unit variance and modelled snowmelt to the results from the 30 m, hourly control test described above. RESULTS Mean and variance of estimated basin SWE Summary statistics describing the test estimates of SWE are shown in Table I. All tests resulted in a reduction in the range of estimated SWE values within the basin; the lower values were particularly a ected. Two-tailed t-tests were performed for each test to determine whether the test SWE was signi cantly di erent from the control SWE of 2.13 m (null hypothesis, H o : SWE test ˆ 2.13 m, 5% signi cance level). The null hypothesis was rejected in the three tests at 90 m spatial resolution, indicating that the estimated means of 2.42±2.52 m were statistically di erent from the control. All the remaining tests failed to reject the null hypothesis. Therefore at 250 and 500 m spatial resolutions, for all three temporal resolutions, the model estimated the correct SWE. F-tests were performed to determine whether the variance of basin SWE (s 2 swe )of each test was signi cantly di erent from the variance of the control of m 2 (H o : s 2 swe ˆ (0.54 m 2 ), 5% signi cance level). The null hypothesis was rejected in all cases except the three at 500 m spatial resolution, where it was narrowly accepted. Overall, the F-tests suggest that the variances of estimated basin SWE at the coarsened spatial resolutions and at the 30 m resolution were not signi cantly di erent.

6 1532 D. CLINE ET AL. Table I. Summary statistics of basin-wide peak accumulation SWE (21 April 1993) for the control and each test Spatial resolution Temporal resolution SWE (m) Percentage di erence Standard deviation Minimum SWE Maximum SWE (m) (h) (%) (m) (m) (m) ± Table II. Comparison of estimated total basin SWE volume with control Spatial resolution Temporal resolution Total basin SWE volume Di erence (m 3 ) Percentage di erence Basin area (m 2 ) Corrected SWE volume (m) (h) (m 3 ) (%) (m 3 ) ± ± Total basin water volume stored as SWE The estimated total volume of water stored as SWE in the basin from each test was computed by summing the volumes from each pixel within the basin, and is compared with the control value in Table II. The computed total basin SWE volumes are too large because changes to the raster depiction of the basin boundaries at coarser spatial resolutions resulted in larger estimates of the basin area at the coarser spatial resolutions. This is evident since the estimated total basin SWE volume normalized by the basin area for the respective spatial resolution is equal to the SWE shown in Table I. Thus the apparent overestimation of the total basin SWE volume in each of the tests is solely an artifact of the raster delineation of basin boundaries in those cases where the estimated SWE was less than the control. When the SWE volumes are corrected by normalizing for the high resolution basin area (Table II), the problem is corrected for the tests at 250 and 500 m. These results are shown to illustrate this potential problem, which could be encountered when modelling at regional scales. In this case, the problem could be easily corrected by using a vector basin boundary delineation to determine the total basin SWE volume. Comparison of spatial patterns of SWE Coarsening the spatial resolution of the model resulted in increasing losses of information about the location of SWE in the basin (Figure 4). To facilitate comparison, the results for each test shown here are

7 SCALE EFFECTS 1533 Figure 4. Modelled SWE distributions at (a) 30 m resolution (control), (b) 90 m, (c) 250 m and (d) 250 m. These results are for the 1 h temporal resolution; di erences between these patterns and the patterns for the 3 h and 6 h resolutions are negligible. Results are standardized to zero mean and unit variance to facilitate comparison; the grey-scale shown is in units of standard deviations away from the mean. The key labels are described in the text standardized to zero mean and unit variance so that each image is displayed with the same grey scale. At each spatial resolution, changes in temporal resolution had only negligible e ects on the spatial patterns of SWE, so are not shown here. The 30 m control image (Figure 4a) shows areas of low SWE on the steep ridge forming the southern and western boundary of the basin (A1, A2), on the ridge forming the extreme northeast boundary of the basin (A3) and on steep cli bands midway up the basin (A4). Areas of large SWE include atter areas at the base of steep slopes (A5), on the valley oor (A6), in a protected area in the upper reaches of the watershed (A7) and on a broad bench on the western side of the basin (A8). At 90 m resolution (Figure 4b), the areas of low SWE are still located along the steep ridges (B1), but to a lesser extent, and on some of the cli areas in the lower part of the basin (B2). The smaller areas of low SWE in the control, such as on the intermediate cli bands, are not estimated at this resolution. Areas of large SWE include the protected region in the upper reaches of the basin (B3) and the broad bench on the western side of the basin (B4). SWE is overestimated on the ridge top itself (B5). Here, slopes are atter in the 90 m model, and as a result are estimated to receive more solar radiation. With more apparent energy available during the same period of time, the model estimates greater SWE. SWE is underestimated on the valley oor (B6). At 250 m resolution (Figure 4c), areas of lowest SWE remain on the extreme north-east and west ridges (C1), and to a lesser extent along the south-east ridge (C2). At this resolution the model estimates less than average SWE across the mid-elevations of the basin (C3), in roughly the same location as the low SWE areas on the cli bands in the control image. The protected areas in the upper reaches of the basin are still estimated to contain larger amounts of SWE (C4), and large SWE values are estimated on the valley oor (C5). With respect to the lower amounts of SWE in the vicinity of the cli bands and the increased SWE on the valley oor, the results of the 250 m resolution model more closely resemble the control than the 90 m results.

8 1534 D. CLINE ET AL. At 500 m resolution (Figure 4d), the depiction of SWE only crudely resembles the control image. Low SWE areas correctly include the western and south-eastern ridges, but because of the large grid scale these low SWE areas are extended too far downslope into areas of the basin that should contain larger SWE amounts (D1). Areas of larger SWE correctly include the valley oor (D2), such as it is depicted at 500 m, and the protected area in the upper reaches of the basin (D3). E ect of spatial and temporal resolution on modelled snowmelt The correct estimation of SWE implicitly suggests that the snowmelt modelled at each pixel from the energy balance is correct, but it is possible that compensating errors over the course of the snowmelt season could produce the same result. To simplify evaluation of distributed snowmelt modelled at the coarser spatial and temporal resolutions, we computed the basin-wide hourly energy balance, converted these hourly totals to mass units and normalized the results to a common basin area of m 2 of the control (Figure 5). The coarser temporal resolutions clearly result in poorer representations of the diurnal snowmelt cycle, although the modelled snowmelt values generally follow the control values at all spatial and temporal resolutions. Hourly root mean squared errors (RMSE) for snowmelt are roughly equivalent at each spatial Figure 5. Examples of three days of modelled snowmelt at (a) 1 h temporal resolution, (b) 3 h and (c) 6 hr. The control values are shown in each plot for comparison

9 SCALE EFFECTS 1535 Table III. RMSE of modelled hourly snowmelt compared with control 1 h tests 3 h tests 6 h tests Spatial resolution RMSE Spatial resolution RMSE Spatial resolution RMSE (m) (m 3 hr 71 ) (m) (m 3 h 71 ) (m) (m 3 hr 71 ) Mean: 648 Mean: 1375 Mean: 2190 resolution, but increase with increasing temporal resolutions (Table III). This is apparent in Figure 5, where the longer time-steps result in greater departures from the control values, especially during the morning. DISCUSSION AND CONCLUSIONS The evidence from the sensitivity analysis presented here strongly indicates that the distribution of SWE and snowmelt can be rigorously estimated using the SNODIS model at spatial and temporal scales conducive to regional-scale modelling. If the objective is to determine the total volume of SWE contained in a basin, reasonable results should be expected using a 500 m and 6 h resolutions. If details of the diurnal timing of snowmelt are required, the 6 h data may be too crude, at least as far as the degradation method we used here is concerned. Averages, or shorter time-steps, would be warranted in that case. It is important to realize that the ELW test basin is very small, and contains a limited distribution of topographical characteristics, most notably aspect. The small basin size becomes a concern at the larger spatial resolutions tested, such as the 500 m resolution where only six grid cells depict the basin. Therefore, we view these results as encouraging `proof of concept', but there is a clear need to test the SNODIS model in a similar fashion over a larger test area. In addition to the study area size, other questions were raised during this study that pertain to the application of this approach over large regions. Of particular interest is why SWE was overestimated at the 90 m resolution but correctly estimated at the larger resolutions. The 90 m resolution results were statistically di erent from the control mean, although the di erences were perhaps not unreasonably large, at 14±17%, Increasing the spatial resolution tended to reduce the elevations of the peaks along the southern and eastern ridges of the basin, e ectively smoothing the sharp ridge to varying degrees (e.g. Figure 2). Some of the steeper, northerly facing slopes were reduced as a result, which tended to increase the modelled insolation on these areas. This would tend to increase estimated SWE in the SNODIS methodology. However, this e ect occurred at each of the larger spatial resolutions, and was observed least in the 90 m case. It is possible that the di erences between the 90 m tests and the others are simply a result of the particular coincidence of slopes, aspects, elevations and snow cover duration that resulted from the spatial resampling to each resolution. Further evaluation of this possibility will require tests to be performed in a larger study area exhibiting a greater range of topographical characteristics. A second possible explanation is a hypothesis that somewhere between 90 m and 250 m a scale threshold exists, below which representation of explicit spatial patterns of the relevant variables matters strongly, and beyond which the explicit distribution of the governing variables becomes relatively unimportant. This would be consistent with the representative elementary area (REA) concept presented by Wood et al. (1988) for catchment-scale storm response modelling. Although our scale sensitivity tests employed a di erent spatial aggregation approach from theirs, fundamentally, our tests represent a similar shift from modelling (snowmelt) processes using explicit spatial detail to modelling them using statistical distributions. If such an REA for snowmelt processes exists, it may actually be preferable to apply the SNODIS model to larger regions using coarser resolution governing data. We cannot conclude the existence of an REA for snowmelt modelling from testing only four spatial resolutions. Additional investigation, again preferably in a test basin with a broader range of conditions, will be necessary in order to address this hypothesis.

10 1536 D. CLINE ET AL. Our method of resampling the subpixel fractional snow cover products ensured that the same amount of snow-covered area existed in the larger pixels as in the total of the incorporated smaller pixels. This e ectively synthesized a subpixel snow fraction product that a spectral mixture model snow classi cation scheme might produce from a coarser resolution sensor. The 250 and 500 m test resolutions correspond to product resolutions that will be available on the MODIS sensor, planned for launch on the EOS AM-1 spacecraft in June The MODIS data should support the determination of subpixel snow cover mapping. An assumption in the SNODIS modelling approach that we did not address here is that the gradual reduction in snow cover fraction over time represents a patch of snow becoming smaller but otherwise not changing location within a pixel. This assumption seems reasonable for small pixels, such as the 30 m or even the 90 m resolutions, but it may become questionable for larger pixel sizes. The assumption apparently was su cient in these tests, but further analysis is warranted before presuming that larger resolution remote sensing data will be suitable for driving SNODIS. ACKNOWLEDGEMENTS This research was supported in part by an interdisciplinary grant under NASA's Earth Observing System program, in part by grant EAR from the National Science Foundation, and by the National Weather Service, O ce of Hydrology, NOAA. REFERENCES Cline, D., Bales, R., and Dozier, J `Estimating the spatial distribution of snow in mountain basins using remote sensing and energy balance modeling'. Wat. Resour. Res., 34, 1275±1285. Dozier, J., and Frew, J `Rapid calculation of terrain parameters for radiation modeling from digital elevation data', IEEE Trans. Geosci. Remote Sens., 28, 963±969. Elder, K `Snow distribution in alpine watersheds', PhD Dissertation, University of California, Santa Barbara. Elder, K., Dozier, J., and Michaelson, J `Snow accumulation and distribution in an alpine watershed', Wat. Resour. Res., 27, 1541±1552. Elder, K., Michaelson, J., and Dozier, J `Small basin modeling of snow water equivalence using binary regression tree methods, in Biogeochemistry of Seasonally Snow-Covered Catchments, IAHS Publ., (edited by Tonnessen, K. A., Williams, M. W., and Tranter, M.), 228, 129±139. Idso, S. B `A set of equations for full spectrum and 8±14 mm and 10.5±12.5 mm thermal radiation from cloudless skies', Wat. Resour. Res., 17, 295±304. Jordan, R `A one-dimensional temperature model for a snow cover', Special Report US Army Cold Regions Research and Engineering Laboratory, Hanover. Melack, J. M., Sickman, J., Leydecker, A., and Marrett, D `Comparative analyses of high-altitude lakes and catchments in the Sierra Nevada: susceptibility to acidi cation', Final Report to the California Air Resources Board, Contract A , Sacramento, CA. Rosenthal, W., and Dozier, J `Automated mapping of montane snow cover at sub-pixel resolution from Landsat Thematic Mapper', Wat. Resour. Res., 32, 115±130. Tonnessen, K. A `The Emerald Lake watershed study: introduction and site description', Wat. Resour. Res., 27, 1537±1539. Wood, E. F., Sivapalan, M., Beven, K. J., and Band, L `E ects of spatial variability and scale with implications to hydrologic modeling', J. Hydrol., 102, 29±47.